Solve frac{2^{30}+2^{24}+2^20}{2^31+2^30-2^29}

$$\frac { 2 ^ { 30 } + 2 ^ { 24 } + 2 ^ { 20 } } { 2 ^ { 31 } + 2 ^ { 30 } - 2 ^ { 29 } }$$

Evaluate

$$\frac{1041}{2560}=0.406640625$$

Solution Steps

Calculate 2 to the power of 30 and get 1073741824.

$$\frac{1073741824+2^{24}+2^{20}}{2^{31}+2^{30}-2^{29}}$$

Calculate 2 to the power of 24 and get 16777216.

$$\frac{1073741824+16777216+2^{20}}{2^{31}+2^{30}-2^{29}}$$

Add 1073741824 and 16777216 to get 1090519040.

$$\frac{1090519040+2^{20}}{2^{31}+2^{30}-2^{29}}$$

Calculate 2 to the power of 20 and get 1048576.

$$\frac{1090519040+1048576}{2^{31}+2^{30}-2^{29}}$$

Add 1090519040 and 1048576 to get 1091567616.

$$\frac{1091567616}{2^{31}+2^{30}-2^{29}}$$

Calculate 2 to the power of 31 and get 2147483648.

$$\frac{1091567616}{2147483648+2^{30}-2^{29}}$$

Calculate 2 to the power of 30 and get 1073741824.

$$\frac{1091567616}{2147483648+1073741824-2^{29}}$$

Add 2147483648 and 1073741824 to get 3221225472.

$$\frac{1091567616}{3221225472-2^{29}}$$

Calculate 2 to the power of 29 and get 536870912.

$$\frac{1091567616}{3221225472-536870912}$$

Subtract 536870912 from 3221225472 to get 2684354560.

$$\frac{1091567616}{2684354560}$$

Reduce the fraction \frac{1091567616}{2684354560} to lowest terms by extracting and canceling out 1048576.

$$\frac{1041}{2560}$$

Factor

$$\frac{3 \cdot 347}{2 ^ {9} \cdot 5} = 0.406640625$$